Question

微分方程问题若P(t)满足且P(0)=25.求P.

Answer 1

dP/[P(75-P)]=0.0003dt

dP/75*[1/P+1/(75-P)]=0.0003dt

ln|P|-ln|75-P|=0.0225t+C0

|P/(75-P)|=Ce^(0.0225t)

代入t=0,P=25,得

C=0.5

P/(75-P)=0.5e^(0.0225t)